arccos

Time bar (total: 7.1s)

analyze5.0ms (0.1%)

Memory
8.8MiB live, 8.8MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%100%0%0%0%0%3
33.3%25%50%0%0%25%0%4
60%37.5%25%0%0%37.5%0%5
77.8%43.7%12.5%0%0%43.7%0%6
88.2%46.9%6.2%0%0%46.9%0%7
93.9%48.4%3.1%0%0%48.4%0%8
96.9%49.2%1.6%0%0%49.2%0%9
98.4%49.6%0.8%0%0%49.6%0%10
99.2%49.8%0.4%0%0%49.8%0%11
99.6%49.9%0.2%0%0%49.9%0%12
Compiler

Compiled 13 to 11 computations (15.4% saved)

sample2.0s (27.7%)

Memory
-5.2MiB live, 1 794.0MiB allocated
Samples
1.6s8 256×0valid
1.0ms21×0invalid
Precisions
Click to see histograms. Total time spent on operations: 1.0s
ival-sub: 304.0ms (29.7% of total)
ival-mult: 276.0ms (27% of total)
ival-add: 235.0ms (23% of total)
ival-atan: 71.0ms (6.9% of total)
ival-sqrt: 68.0ms (6.6% of total)
ival-div: 53.0ms (5.2% of total)
exact: 7.0ms (0.7% of total)
ival-true: 6.0ms (0.6% of total)
ival-assert: 3.0ms (0.3% of total)
Bogosity

preprocess43.0ms (0.6%)

Memory
23.4MiB live, 101.6MiB allocated
Algorithm
1×egg-herbie
Rules
208×lower-fma.f64
208×lower-fma.f32
132×lower-*.f32
130×lower-*.f64
84×times-frac
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01124
13122
25922
310822
418022
535022
662022
764722
0911
01511
12411
23011
34111
46411
59811
613511
720811
833011
949811
1052911
052911
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))

explain98.0ms (1.4%)

Memory
9.5MiB live, 286.6MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
00-0-#s(literal 1 binary64)
00-0-(-.f64 #s(literal 1 binary64) x)
00-0-(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
00-0-(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
00-0-(+.f64 #s(literal 1 binary64) x)
00-0-(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
00-0-#s(literal 2 binary64)
00-0-x
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
37.0ms512×0valid
Compiler

Compiled 116 to 40 computations (65.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 23.0ms
ival-atan: 5.0ms (21.5% of total)
ival-div: 4.0ms (17.2% of total)
ival-add: 4.0ms (17.2% of total)
ival-sqrt: 4.0ms (17.2% of total)
ival-mult: 3.0ms (12.9% of total)
ival-sub: 3.0ms (12.9% of total)
exact: 1.0ms (4.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune2.0ms (0%)

Memory
-37.5MiB live, 1.9MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Compiler

Compiled 12 to 9 computations (25% saved)

simplify24.0ms (0.3%)

Memory
12.6MiB live, 54.7MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
✓cost-diff0
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
✓cost-diff0
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Rules
208×lower-fma.f64
208×lower-fma.f32
132×lower-*.f32
130×lower-*.f64
74×div-sub
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0944
01544
12444
23044
34144
46444
59844
613544
720844
833044
949844
1052944
052944
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
#s(literal 2 binary64)
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(+.f64 #s(literal 1 binary64) x)
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
#s(literal 2 binary64)
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(+.f64 #s(literal 1 binary64) x)

localize32.0ms (0.4%)

Memory
-9.9MiB live, 67.3MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓accuracy100.0%
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
✓accuracy100.0%
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
Samples
17.0ms256×0valid
Compiler

Compiled 46 to 11 computations (76.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-div: 2.0ms (19.2% of total)
ival-mult: 2.0ms (19.2% of total)
ival-atan: 2.0ms (19.2% of total)
ival-sqrt: 2.0ms (19.2% of total)
ival-add: 1.0ms (9.6% of total)
ival-sub: 1.0ms (9.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory
8.6MiB live, 8.6MiB allocated
Counts
4 → 48
Calls
Call 1
Inputs
#<alt (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))>
#<alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))>
#<alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))>
#<alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))>
Outputs
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (/ 1 (* x (sqrt -1))))>
#<alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))>
#<alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (/ 1 (* x (sqrt -1))))>
#<alt (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))>
#<alt (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))>
#<alt 1>
#<alt (+ 1 (* -2 x))>
#<alt (+ 1 (* x (- (* 2 x) 2)))>
#<alt (+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))>
#<alt -1>
#<alt (- (* 2 (/ 1 x)) 1)>
#<alt (- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))>
#<alt (- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))>
#<alt -1>
#<alt (- (* 2 (/ 1 x)) 1)>
#<alt (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)>
#<alt (- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)>
Calls

12 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms
x
@-inf
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
0.0ms
x
@inf
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
0.0ms
x
@-inf
(sqrt (/ (- 1 x) (+ 1 x)))
0.0ms
x
@0
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

rewrite287.0ms (4.1%)

Memory
0.0MiB live, 360.5MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
2 152×lower-fma.f64
2 152×lower-fma.f32
2 042×lower-*.f32
2 040×lower-*.f64
1 870×lower-/.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0935
01536
15236
233936
345898
098248
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 7
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(atan.f64 #s(literal 1 binary64))
(neg.f64 (atan.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
(neg.f64 (atan.f64 (/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
#s(literal 1 binary64)
#s(literal 1 binary64)

simplify265.0ms (3.7%)

Memory
29.7MiB live, 548.2MiB allocated
Algorithm
1×egg-herbie
Rules
10 954×lower-fma.f64
10 954×lower-fma.f32
2 906×lower-*.f64
2 906×lower-*.f32
1 802×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0107541
1276480
2764466
32114454
46114448
08084437
Stop Event
1×iter limit
1×node limit
Counts
48 → 48
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
1
(+ 1 (* -2 x))
(+ 1 (* x (- (* 2 x) 2)))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
-1
(- (* 2 (/ 1 x)) 1)
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
-1
(- (* 2 (/ 1 x)) 1)
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(+.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) (*.f64 x x))))
1
#s(literal 1 binary64)
(+ 1 (* -2 x))
(fma.f64 x #s(literal -2 binary64) #s(literal 1 binary64))
(+ 1 (* x (- (* 2 x) 2)))
(fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -2 binary64) #s(literal 2 binary64)) #s(literal -2 binary64)) #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (* 2 (/ 1 x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) x))
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x)) x))
-1
#s(literal -1 binary64)
(- (* 2 (/ 1 x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) x))
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x))
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x)) x))

eval6.0ms (0.1%)

Memory
-25.2MiB live, 14.3MiB allocated
Compiler

Compiled 602 to 103 computations (82.9% saved)

prune6.0ms (0.1%)

Memory
18.3MiB live, 18.3MiB allocated
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New50555
Fresh000
Picked011
Done000
Total50656
Accuracy
100.0%
Counts
56 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶98.6%
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
▶99.7%
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
▶99.6%
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
▶99.4%
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
▶99.6%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))))
✓100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Compiler

Compiled 110 to 89 computations (19.1% saved)

simplify180.0ms (2.5%)

Memory
13.5MiB live, 127.5MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))
✓cost-diff0
(sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))
✓cost-diff0
(atan.f64 (sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))))
✓cost-diff0
(fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))
✓cost-diff0
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
✓cost-diff0
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
✓cost-diff0
(-.f64 #s(literal 1 binary64) x)
✓cost-diff0
(atan.f64 (-.f64 #s(literal 1 binary64) x))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
✓cost-diff0
(atan.f64 #s(literal 1 binary64))
✓cost-diff0
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
✓cost-diff0
(fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))
✓cost-diff0
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
✓cost-diff0
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
Rules
3 352×lower-fma.f32
3 338×lower-fma.f64
988×lower-*.f32
978×lower-*.f64
560×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
026152
052152
196152
2166152
3237152
4339152
5567152
61090152
71951152
82338152
92532152
102649152
112751152
122791152
132824152
142829152
152829152
162837152
02837152
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
#s(literal 2 binary64)
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
x
(fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(atan.f64 #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
#s(literal 2 binary64)
(atan.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
#s(literal 2 binary64)
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
x
(fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))
#s(literal 1/2 binary64)
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))))
#s(literal 2 binary64)
(atan.f64 (sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))))
(sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))
x
(fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64))
#s(literal -2 binary64)
#s(literal 1 binary64)
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
#s(literal 2 binary64)
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
x
(fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
(atan.f64 #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
#s(literal 2 binary64)
(atan.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
#s(literal 2 binary64)
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
x
(fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))
#s(literal 1/2 binary64)
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))))
#s(literal 2 binary64)
(atan.f64 (sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))))
(sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))
x
(fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64))
#s(literal -2 binary64)
#s(literal 1 binary64)

localize97.0ms (1.4%)

Memory
-12.9MiB live, 222.0MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64))
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))))
✓accuracy100.0%
(atan.f64 (sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))))
✓accuracy100.0%
(sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))
✓accuracy100.0%
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
✓accuracy100.0%
(fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
✓accuracy100.0%
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
✓accuracy100.0%
(-.f64 #s(literal 1 binary64) x)
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
✓accuracy100.0%
(atan.f64 (-.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
✓accuracy100.0%
(atan.f64 #s(literal 1 binary64))
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
✓accuracy100.0%
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
✓accuracy100.0%
(fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))
✓accuracy100.0%
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
Samples
57.0ms256×0valid
Compiler

Compiled 182 to 35 computations (80.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 39.0ms
ival-mult: 17.0ms (43.7% of total)
ival-add: 10.0ms (25.7% of total)
ival-atan: 9.0ms (23.1% of total)
ival-sqrt: 2.0ms (5.1% of total)
ival-sub: 1.0ms (2.6% of total)
exact: 1.0ms (2.6% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series15.0ms (0.2%)

Memory
-18.4MiB live, 19.7MiB allocated
Counts
18 → 192
Calls
Call 1
Inputs
#<alt (*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))>
#<alt (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))>
#<alt (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))>
#<alt (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))>
#<alt (*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))>
#<alt (atan.f64 #s(literal 1 binary64))>
#<alt (*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))>
#<alt (atan.f64 (-.f64 #s(literal 1 binary64) x))>
#<alt (-.f64 #s(literal 1 binary64) x)>
#<alt (*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))>
#<alt (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))>
#<alt (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))>
#<alt (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))>
#<alt (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))))>
#<alt (atan.f64 (sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))))>
#<alt (sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))>
#<alt (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))>
#<alt (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64))>
Outputs
#<alt (* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))>
#<alt (* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))>
#<alt (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))>
#<alt (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))>
#<alt (* -1/2 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))>
#<alt -1>
#<alt (- (* 1/2 x) 1)>
#<alt (- (* x (+ 1/2 (* -1/2 x))) 1)>
#<alt (- (* x (+ 1/2 (* -1/2 x))) 1)>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 2) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/2))>
#<alt (* (pow x 2) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/2))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (+ 1 (* -1 x))))>
#<alt (* 2 (atan (+ 1 (* -1 x))))>
#<alt (* 2 (atan (+ 1 (* -1 x))))>
#<alt (* 2 (atan (+ 1 (* -1 x))))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (+ 1 (* -1 x)))>
#<alt (atan (+ 1 (* -1 x)))>
#<alt (atan (+ 1 (* -1 x)))>
#<alt (atan (+ 1 (* -1 x)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))>
#<alt (atan (+ 1 (* x (- (* 1/2 x) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 x) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 x) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 x) 1))))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))>
#<alt (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))>
#<alt (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))>
#<alt (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))>
#<alt (* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))>
#<alt (* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))>
#<alt -1>
#<alt (- (* 1/2 x) 1)>
#<alt (- (* 1/2 x) 1)>
#<alt (- (* 1/2 x) 1)>
#<alt (* 1/2 x)>
#<alt (* x (- 1/2 (/ 1 x)))>
#<alt (* x (- 1/2 (/ 1 x)))>
#<alt (* x (- 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* -1 (* x (- (/ 1 x) 1/2)))>
#<alt (* -1 (* x (- (/ 1 x) 1/2)))>
#<alt (* -1 (* x (- (/ 1 x) 1/2)))>
#<alt (* 2 (atan (sqrt (+ 1 (* x (- (* 2 x) 2))))))>
#<alt (* 2 (atan (sqrt (+ 1 (* x (- (* 2 x) 2))))))>
#<alt (* 2 (atan (sqrt (+ 1 (* x (- (* 2 x) 2))))))>
#<alt (* 2 (atan (sqrt (+ 1 (* x (- (* 2 x) 2))))))>
#<alt (* 2 (atan (sqrt (- (+ 1 (* 2 (pow x 2))) (* 2 x)))))>
#<alt (* 2 (atan (sqrt (- (+ 1 (* 2 (pow x 2))) (* 2 x)))))>
#<alt (* 2 (atan (sqrt (- (+ 1 (* 2 (pow x 2))) (* 2 x)))))>
#<alt (* 2 (atan (sqrt (- (+ 1 (* 2 (pow x 2))) (* 2 x)))))>
#<alt (* 2 (atan (sqrt (+ 1 (+ (* -2 x) (* 2 (pow x 2)))))))>
#<alt (* 2 (atan (sqrt (+ 1 (+ (* -2 x) (* 2 (pow x 2)))))))>
#<alt (* 2 (atan (sqrt (+ 1 (+ (* -2 x) (* 2 (pow x 2)))))))>
#<alt (* 2 (atan (sqrt (+ 1 (+ (* -2 x) (* 2 (pow x 2)))))))>
#<alt (atan (sqrt (+ 1 (* x (- (* 2 x) 2)))))>
#<alt (atan (sqrt (+ 1 (* x (- (* 2 x) 2)))))>
#<alt (atan (sqrt (+ 1 (* x (- (* 2 x) 2)))))>
#<alt (atan (sqrt (+ 1 (* x (- (* 2 x) 2)))))>
#<alt (atan (sqrt (- (+ 1 (* 2 (pow x 2))) (* 2 x))))>
#<alt (atan (sqrt (- (+ 1 (* 2 (pow x 2))) (* 2 x))))>
#<alt (atan (sqrt (- (+ 1 (* 2 (pow x 2))) (* 2 x))))>
#<alt (atan (sqrt (- (+ 1 (* 2 (pow x 2))) (* 2 x))))>
#<alt (atan (sqrt (+ 1 (+ (* -2 x) (* 2 (pow x 2))))))>
#<alt (atan (sqrt (+ 1 (+ (* -2 x) (* 2 (pow x 2))))))>
#<alt (atan (sqrt (+ 1 (+ (* -2 x) (* 2 (pow x 2))))))>
#<alt (atan (sqrt (+ 1 (+ (* -2 x) (* 2 (pow x 2))))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* x (+ 1/2 (* 1/2 x))) 1)))>
#<alt (* x (sqrt 2))>
#<alt (* x (- (sqrt 2) (/ 1 (* x (sqrt 2)))))>
#<alt (* x (- (+ (sqrt 2) (* 1/2 (/ (- 1 (/ 1 (pow (sqrt 2) 2))) (* (pow x 2) (sqrt 2))))) (/ 1 (* x (sqrt 2)))))>
#<alt (* x (- (+ (sqrt 2) (+ (* 1/2 (/ (- 1 (/ 1 (pow (sqrt 2) 2))) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (- 1 (/ 1 (pow (sqrt 2) 2))) (* (pow x 3) (pow (sqrt 2) 3)))))) (/ 1 (* x (sqrt 2)))))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (- (sqrt 2) (/ 1 (* x (sqrt 2))))))>
#<alt (* -1 (* x (+ (sqrt 2) (* -1 (/ (+ (* -1/2 (/ (- 1 (/ 1 (pow (sqrt 2) 2))) (* x (sqrt 2)))) (/ 1 (sqrt 2))) x)))))>
#<alt (* -1 (* x (+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (/ 1 (pow (sqrt 2) 4)) (/ 1 (pow (sqrt 2) 2))) (* x (sqrt 2)))) (* 1/2 (/ (- 1 (/ 1 (pow (sqrt 2) 2))) (sqrt 2)))) x)) (/ 1 (sqrt 2))) x)))))>
#<alt 1>
#<alt (+ 1 (* -2 x))>
#<alt (+ 1 (* x (- (* 2 x) 2)))>
#<alt (+ 1 (* x (- (* 2 x) 2)))>
#<alt (* 2 (pow x 2))>
#<alt (* (pow x 2) (- 2 (* 2 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 2 (/ 1 (pow x 2))) (* 2 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 2 (/ 1 (pow x 2))) (* 2 (/ 1 x))))>
#<alt (* 2 (pow x 2))>
#<alt (* (pow x 2) (- 2 (* 2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 2 (* -1 (/ (- 2 (/ 1 x)) x))))>
#<alt (* (pow x 2) (+ 2 (* -1 (/ (- 2 (/ 1 x)) x))))>
#<alt -2>
#<alt (- (* 2 x) 2)>
#<alt (- (* 2 x) 2)>
#<alt (- (* 2 x) 2)>
#<alt (* 2 x)>
#<alt (* x (- 2 (* 2 (/ 1 x))))>
#<alt (* x (- 2 (* 2 (/ 1 x))))>
#<alt (* x (- 2 (* 2 (/ 1 x))))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 2 (/ 1 x)) 2)))>
#<alt (* -1 (* x (- (* 2 (/ 1 x)) 2)))>
#<alt (* -1 (* x (- (* 2 (/ 1 x)) 2)))>
Calls

48 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(* 2 (atan (+ (* x (+ (* x 1/2) -1)) 1)))
1.0ms
x
@-inf
(* 2 (atan (+ (* x (+ (* x (+ (* x -1/2) 1/2)) -1)) 1)))
1.0ms
x
@inf
(* 2 (atan (+ (* x (+ (* x (+ (* x -1/2) 1/2)) -1)) 1)))
0.0ms
x
@inf
(sqrt (+ (* x (+ (* 2 x) -2)) 1))
0.0ms
x
@-inf
(* 2 (atan (sqrt (+ (* x (+ (* 2 x) -2)) 1))))

rewrite395.0ms (5.6%)

Memory
-6.5MiB live, 437.2MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 684×lower-/.f64
4 684×lower-*.f32
4 684×lower-/.f32
4 674×lower-*.f64
4 186×lower-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
026128
052128
1190128
21375128
08528128
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
18 → 386
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(atan.f64 #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(atan.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))))
(atan.f64 (sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))))
(sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(*.f64 (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))) #s(literal 2 binary64))
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(+.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) #s(literal 1 binary64))
(+.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))
(+.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))))
(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (neg.f64 x))
(-.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) x)
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (/.f64 (*.f64 (*.f64 x x) (*.f64 (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 x (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) x))
(fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 x x) (-.f64 #s(literal 1 binary64) x))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x (-.f64 #s(literal 1 binary64) x))
(fma.f64 (*.f64 (*.f64 x x) (*.f64 (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) x))
(fma.f64 (fma.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (*.f64 x (*.f64 x x)) (neg.f64 (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (-.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (neg.f64 x))))) #s(literal 1 binary64))
(fma.f64 (fma.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (neg.f64 (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (neg.f64 x))) #s(literal 1 binary64))
(fma.f64 (*.f64 x (fma.f64 (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (neg.f64 (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #s(literal 1 binary64))
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(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) #s(literal -8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) #s(literal 4 binary64)) (*.f64 x #s(literal -4 binary64))))))
(*.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)))))
(*.f64 (-.f64 #s(literal 4 binary64) (*.f64 #s(literal 4 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) x))))

simplify2.0s (28.7%)

Memory
2.7MiB live, 551.6MiB allocated
Algorithm
1×egg-herbie
Rules
11 762×lower-fma.f64
11 762×lower-fma.f32
3 220×lower-*.f64
3 220×lower-*.f32
3 082×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01851754
15001699
214991679
341341664
082281409
Stop Event
1×iter limit
1×node limit
Counts
192 → 192
Calls
Call 1
Inputs
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))
(atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))
(atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))
(atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* -1/2 (pow x 3))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
-1
(- (* 1/2 x) 1)
(- (* x (+ 1/2 (* -1/2 x))) 1)
(- (* x (+ 1/2 (* -1/2 x))) 1)
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 2) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/2))
(* (pow x 2) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/2))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (+ 1 (* -1 x))))
(* 2 (atan (+ 1 (* -1 x))))
(* 2 (atan (+ 1 (* -1 x))))
(* 2 (atan (+ 1 (* -1 x))))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (+ 1 (* -1 x)))
(atan (+ 1 (* -1 x)))
(atan (+ 1 (* -1 x)))
(atan (+ 1 (* -1 x)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))
(* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))
(* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))
(* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(atan (+ 1 (* x (- (* 1/2 x) 1))))
(atan (+ 1 (* x (- (* 1/2 x) 1))))
(atan (+ 1 (* x (- (* 1/2 x) 1))))
(atan (+ 1 (* x (- (* 1/2 x) 1))))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* 1/2 x) 1)))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
-1
(- (* 1/2 x) 1)
(- (* 1/2 x) 1)
(- (* 1/2 x) 1)
(* 1/2 x)
(* x (- 1/2 (/ 1 x)))
(* x (- 1/2 (/ 1 x)))
(* x (- 1/2 (/ 1 x)))
(* 1/2 x)
(* -1 (* x (- (/ 1 x) 1/2)))
(* -1 (* x (- (/ 1 x) 1/2)))
(* -1 (* x (- (/ 1 x) 1/2)))
(* 2 (atan (sqrt (+ 1 (* x (- (* 2 x) 2))))))
(* 2 (atan (sqrt (+ 1 (* x (- (* 2 x) 2))))))
(* 2 (atan (sqrt (+ 1 (* x (- (* 2 x) 2))))))
(* 2 (atan (sqrt (+ 1 (* x (- (* 2 x) 2))))))
(* 2 (atan (sqrt (- (+ 1 (* 2 (pow x 2))) (* 2 x)))))
(* 2 (atan (sqrt (- (+ 1 (* 2 (pow x 2))) (* 2 x)))))
(* 2 (atan (sqrt (- (+ 1 (* 2 (pow x 2))) (* 2 x)))))
(* 2 (atan (sqrt (- (+ 1 (* 2 (pow x 2))) (* 2 x)))))
(* 2 (atan (sqrt (+ 1 (+ (* -2 x) (* 2 (pow x 2)))))))
(* 2 (atan (sqrt (+ 1 (+ (* -2 x) (* 2 (pow x 2)))))))
(* 2 (atan (sqrt (+ 1 (+ (* -2 x) (* 2 (pow x 2)))))))
(* 2 (atan (sqrt (+ 1 (+ (* -2 x) (* 2 (pow x 2)))))))
(atan (sqrt (+ 1 (* x (- (* 2 x) 2)))))
(atan (sqrt (+ 1 (* x (- (* 2 x) 2)))))
(atan (sqrt (+ 1 (* x (- (* 2 x) 2)))))
(atan (sqrt (+ 1 (* x (- (* 2 x) 2)))))
(atan (sqrt (- (+ 1 (* 2 (pow x 2))) (* 2 x))))
(atan (sqrt (- (+ 1 (* 2 (pow x 2))) (* 2 x))))
(atan (sqrt (- (+ 1 (* 2 (pow x 2))) (* 2 x))))
(atan (sqrt (- (+ 1 (* 2 (pow x 2))) (* 2 x))))
(atan (sqrt (+ 1 (+ (* -2 x) (* 2 (pow x 2))))))
(atan (sqrt (+ 1 (+ (* -2 x) (* 2 (pow x 2))))))
(atan (sqrt (+ 1 (+ (* -2 x) (* 2 (pow x 2))))))
(atan (sqrt (+ 1 (+ (* -2 x) (* 2 (pow x 2))))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* 1/2 x))) 1)))
(* x (sqrt 2))
(* x (- (sqrt 2) (/ 1 (* x (sqrt 2)))))
(* x (- (+ (sqrt 2) (* 1/2 (/ (- 1 (/ 1 (pow (sqrt 2) 2))) (* (pow x 2) (sqrt 2))))) (/ 1 (* x (sqrt 2)))))
(* x (- (+ (sqrt 2) (+ (* 1/2 (/ (- 1 (/ 1 (pow (sqrt 2) 2))) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (- 1 (/ 1 (pow (sqrt 2) 2))) (* (pow x 3) (pow (sqrt 2) 3)))))) (/ 1 (* x (sqrt 2)))))
(* -1 (* x (sqrt 2)))
(* -1 (* x (- (sqrt 2) (/ 1 (* x (sqrt 2))))))
(* -1 (* x (+ (sqrt 2) (* -1 (/ (+ (* -1/2 (/ (- 1 (/ 1 (pow (sqrt 2) 2))) (* x (sqrt 2)))) (/ 1 (sqrt 2))) x)))))
(* -1 (* x (+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (/ 1 (pow (sqrt 2) 4)) (/ 1 (pow (sqrt 2) 2))) (* x (sqrt 2)))) (* 1/2 (/ (- 1 (/ 1 (pow (sqrt 2) 2))) (sqrt 2)))) x)) (/ 1 (sqrt 2))) x)))))
1
(+ 1 (* -2 x))
(+ 1 (* x (- (* 2 x) 2)))
(+ 1 (* x (- (* 2 x) 2)))
(* 2 (pow x 2))
(* (pow x 2) (- 2 (* 2 (/ 1 x))))
(* (pow x 2) (- (+ 2 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(* (pow x 2) (- (+ 2 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(* 2 (pow x 2))
(* (pow x 2) (- 2 (* 2 (/ 1 x))))
(* (pow x 2) (+ 2 (* -1 (/ (- 2 (/ 1 x)) x))))
(* (pow x 2) (+ 2 (* -1 (/ (- 2 (/ 1 x)) x))))
-2
(- (* 2 x) 2)
(- (* 2 x) 2)
(- (* 2 x) 2)
(* 2 x)
(* x (- 2 (* 2 (/ 1 x))))
(* x (- 2 (* 2 (/ 1 x))))
(* x (- 2 (* 2 (/ 1 x))))
(* 2 x)
(* -1 (* x (- (* 2 (/ 1 x)) 2)))
(* -1 (* x (- (* 2 (/ 1 x)) 2)))
(* -1 (* x (- (* 2 (/ 1 x)) 2)))
Outputs
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(* -1/2 (pow x 3))
(*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 x (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(* -1/2 (pow x 3))
(*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(*.f64 x (*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (* 1/2 x) 1)
(fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))
(- (* x (+ 1/2 (* -1/2 x))) 1)
(fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(- (* x (+ 1/2 (* -1/2 x))) 1)
(fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(* -1/2 (pow x 2))
(*.f64 #s(literal -1/2 binary64) (*.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(* -1/2 (pow x 2))
(*.f64 #s(literal -1/2 binary64) (*.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/2))
(fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(* (pow x 2) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/2))
(fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (- 1 x)))
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1
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1
#s(literal 1 binary64)
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-2
#s(literal -2 binary64)
(- (* 2 x) 2)
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eval83.0ms (1.2%)

Memory
-10.5MiB live, 184.2MiB allocated
Compiler

Compiled 14 235 to 2 097 computations (85.3% saved)

prune49.0ms (0.7%)

Memory
-4.3MiB live, 112.0MiB allocated
Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New5771578
Fresh000
Picked145
Done011
Total5786584
Accuracy
100.0%
Counts
584 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓98.6%
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
▶99.6%
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))
✓99.7%
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
✓99.6%
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
✓99.4%
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
✓100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Compiler

Compiled 61 to 49 computations (19.7% saved)

simplify34.0ms (0.5%)

Memory
8.8MiB live, 59.5MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x)))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))
✓cost-diff128
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))
Rules
504×lower-fma.f32
502×lower-fma.f64
220×lower-*.f32
216×lower-*.f64
128×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0938
01538
12638
23938
37138
412138
524438
643738
754238
856638
956638
056635
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))
#s(literal 2 binary64)
(atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x)))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))
(*.f64 x x)
x
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
#s(literal 2 binary64)
(atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x)))
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)

localize29.0ms (0.4%)

Memory
9.0MiB live, 83.1MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))
✓accuracy100.0%
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x)))
Samples
19.0ms256×0valid
Compiler

Compiled 43 to 12 computations (72.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-mult: 6.0ms (49.4% of total)
ival-atan: 3.0ms (24.7% of total)
ival-sub: 2.0ms (16.5% of total)
ival-add: 1.0ms (8.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series2.0ms (0%)

Memory
6.0MiB live, 6.0MiB allocated
Counts
4 → 48
Calls
Call 1
Inputs
#<alt (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))>
#<alt (*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))>
#<alt (atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x)))>
#<alt (*.f64 x x)>
Outputs
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))>
#<alt (* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))>
#<alt (* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))>
#<alt (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))>
#<alt (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))>
#<alt (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
Calls

12 calls:

TimeVariablePointExpression
0.0ms
x
@0
(* 2 (atan (+ (* (* x x) 1/2) (- 1 x))))
0.0ms
x
@inf
(* 2 (atan (+ (* (* x x) 1/2) (- 1 x))))
0.0ms
x
@-inf
(* 2 (atan (+ (* (* x x) 1/2) (- 1 x))))
0.0ms
x
@0
(* x x)
0.0ms
x
@inf
(* x x)

rewrite314.0ms (4.4%)

Memory
27.4MiB live, 588.3MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
7 208×lower-fma.f32
7 206×lower-fma.f64
4 392×lower-*.f32
4 388×lower-*.f64
2 094×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0931
01531
15131
236631
3537431
0918531
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 168
Calls
Call 1
Inputs
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))
(atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x)))
(*.f64 x x)
Outputs
(+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) (neg.f64 x)))
(+.f64 #s(literal 1 binary64) (neg.f64 (+.f64 x (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))))
(+.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
(+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) x))
(+.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(+.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (+.f64 x #s(literal 1 binary64)))
(+.f64 (neg.f64 x) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(+.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
(+.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (neg.f64 x))
(+.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))))
(+.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) (neg.f64 x)) #s(literal 1 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64))))) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (+.f64 x (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))
(-.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))) (-.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))))
(-.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (-.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))))
(-.f64 (/.f64 (*.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(-.f64 (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (+.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (+.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (*.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64)))) (/.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64)))))
(-.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 x #s(literal 1 binary64))))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))))
(-.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))) (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))))
(-.f64 (+.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 0 binary64)) x)
(fma.f64 x #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) (+.f64 x #s(literal 1 binary64)))
(fma.f64 x #s(literal -1 binary64) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(fma.f64 x (/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))))
(fma.f64 x (exp.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))) (+.f64 x #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))))
(fma.f64 (*.f64 x x) (exp.f64 (log.f64 #s(literal 1/2 binary64))) (+.f64 x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (+.f64 x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x x)))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))))
(fma.f64 #s(literal 1 binary64) x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (+.f64 x #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (neg.f64 x) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))
(fma.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))))
(fma.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) (+.f64 x #s(literal 1 binary64)))) (neg.f64 (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))))
(fma.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (neg.f64 x) #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) x (+.f64 x #s(literal 1 binary64)))
(fma.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (+.f64 #s(literal -1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 x) #s(literal -1 binary64))) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))) x)
(fma.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))) (neg.f64 x))
(fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/4 binary64) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1 binary64) x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
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(*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) (+.f64 x #s(literal 1 binary64)))))
(*.f64 (neg.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))))
(*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) (+.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) (+.f64 x #s(literal 1 binary64)))))
(*.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))))
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) (+.f64 x #s(literal 1 binary64)))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))))
(*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64)))))
(*.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))))
(*.f64 (/.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))) (fma.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (*.f64 (*.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) (+.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) (+.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/64 binary64)))))) (fma.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))))) (*.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/16 binary64))))
(*.f64 (/.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))) (*.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) (*.f64 (+.f64 (neg.f64 x) #s(literal -1 binary64)) (+.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))))) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) (*.f64 (+.f64 (neg.f64 x) #s(literal -1 binary64)) (+.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))))
(*.f64 (/.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64)))))
(*.f64 (atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64)))) #s(literal 2 binary64))
(atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64))))
(neg.f64 (atan.f64 (/.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))))))
(neg.f64 (atan.f64 (/.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) (+.f64 x #s(literal 1 binary64))))))
(neg.f64 (atan.f64 (/.f64 (neg.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))))
(neg.f64 (atan.f64 (/.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 1 binary64))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) (+.f64 x #s(literal 1 binary64)))) (+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(neg.f64 (*.f64 x (neg.f64 x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 #s(literal -1 binary64) (*.f64 x (neg.f64 x)))
(*.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) x)

simplify354.0ms (5%)

Memory
0.4MiB live, 232.4MiB allocated
Algorithm
1×egg-herbie
Rules
4 690×lower-fma.f64
4 690×lower-fma.f32
4 118×lower-*.f64
4 118×lower-*.f32
1 760×cube-prod
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033387
177386
2156386
3361386
4834382
51685382
62530382
73281382
84112382
94799382
105824382
116996382
127958382
08031320
Stop Event
1×iter limit
1×node limit
Counts
48 → 48
Calls
Call 1
Inputs
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* 1/2 x) 1)))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(* 1/2 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/2 binary64)))
(* (pow x 2) (- 1/2 (/ 1 x)))
(*.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(* 1/2 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/2 binary64)))
(* (pow x 2) (- 1/2 (/ 1 x)))
(*.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
(atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval30.0ms (0.4%)

Memory
12.6MiB live, 53.4MiB allocated
Compiler

Compiled 6 609 to 780 computations (88.2% saved)

prune25.0ms (0.4%)

Memory
-20.1MiB live, 55.0MiB allocated
Pruning

6 alts after pruning (0 fresh and 6 done)

PrunedKeptTotal
New2160216
Fresh000
Picked011
Done055
Total2166222
Accuracy
100.0%
Counts
222 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓98.6%
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
✓99.6%
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))
✓99.7%
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
✓99.6%
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
✓99.4%
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
✓100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Compiler

Compiled 128 to 84 computations (34.4% saved)

regimes12.0ms (0.2%)

Memory
23.6MiB live, 23.6MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Calls

5 calls:

3.0ms
x
2.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
2.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
2.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
100.0%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
100.0%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
100.0%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes12.0ms (0.2%)

Memory
-12.5MiB live, 26.1MiB allocated
Counts
6 → 1
Calls
Call 1
Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
Calls

5 calls:

3.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2.0ms
x
2.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
2.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
2.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
99.7%1x
99.7%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
99.7%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
99.7%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
99.7%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes9.0ms (0.1%)

Memory
22.3MiB live, 22.3MiB allocated
Counts
4 → 1
Calls
Call 1
Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))
Calls

5 calls:

2.0ms
x
2.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
99.6%1x
99.6%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
99.6%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
99.6%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
99.6%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes10.0ms (0.1%)

Memory
-23.0MiB live, 20.2MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
Calls

5 calls:

4.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
2.0ms
x
1.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
99.6%1x
99.6%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
99.6%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
99.6%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
99.6%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes6.0ms (0.1%)

Memory
16.7MiB live, 16.7MiB allocated
Counts
2 → 1
Calls
Call 1
Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
Calls

5 calls:

1.0ms
x
1.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
99.4%1x
99.4%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
99.4%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
99.4%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
99.4%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes6.0ms (0.1%)

Memory
-24.8MiB live, 14.5MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
Outputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
Calls

5 calls:

2.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms
x
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
98.6%1x
98.6%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
98.6%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
98.6%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
98.6%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 41 to 28 computations (31.7% saved)

simplify8.0ms (0.1%)

Memory
16.9MiB live, 16.9MiB allocated
Algorithm
1×egg-herbie
Rules
14×*-commutative_binary64
6×+-commutative_binary64
4×sub-neg_binary64
2×1-exp_binary64
2×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02955
14155
24455
34655
44755
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))

soundness583.0ms (8.3%)

Memory
-26.1MiB live, 386.6MiB allocated
Rules
10 954×lower-fma.f64
10 954×lower-fma.f32
4 684×lower-/.f64
4 684×lower-*.f32
4 684×lower-/.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
026128
052128
1190128
21375128
08528128
0935
01536
15236
233936
345898
098248
0107541
1276480
2764466
32114454
46114448
08084437
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
Compiler

Compiled 111 to 73 computations (34.2% saved)

preprocess59.0ms (0.8%)

Memory
16.2MiB live, 130.2MiB allocated
Compiler

Compiled 136 to 76 computations (44.1% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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